2 Tables

This document explains how to reproduce the tables presented in the paper.

3 Install Packages

We install the following packages using the groundhog package manager to increase computational reproducibility.

options(repos = c(CRAN = "https://cran.r-project.org")) 


if (!requireNamespace("groundhog", quietly = TRUE)) {
    install.packages("groundhog")
}

pkgs <- c("magrittr", "data.table", "stringr", "lubridate", "knitr", 
          "sandwich", "lmtest",
          "sjPlot", "stargazer")

groundhog::groundhog.library(pkg = pkgs,
                             date = "2024-08-01")

rm(pkgs)

3.1 Read Data

# data <- data.table::fread(file = "../data/processed/full.csv")
data <- readRDS(file="../data/processed/full.Rda")

data[, communication := as.factor(communication)]
data[, communication := factor(communication, levels = c("point", "interval", "both"))]

3.2 Table 2

This table was created in a manual process, the corresponding summary statistics can be queried using the following code, where surprise == FALSE selects the confirmation treatment arm:

data[communication == "point" & surprise == FALSE,      # choose condition
     .(mean = round(mean(b, na.rm = TRUE), digits = 2), # choose variable
       sd = round(sd(b, na.rm = TRUE), digits = 2)),    # choose variable
     by = stage] %>% 
  kable()

stage	mean	sd
1	-0.05	0.27
2	-0.09	0.31

The number of observations by treatment can be queried using the following code:

data[, 
     .(N = length(unique(participant.label))), 
     by = c("communication", "surprise")][order(surprise, communication)] %>%
  kable()

communication	surprise	N
point	FALSE	255
interval	FALSE	243
both	FALSE	247
point	TRUE	252
interval	TRUE	258
both	TRUE	250

# alternatively:
# data[stage == 2, 
#      .N, 
#      by = c("communication", "surprise")][order(surprise, communication)]

3.3 Table 3

ols_3_1 <- lm(formula = b ~ age_35_52 + age_53_plus + female + high_education + high_income + 
    married + parentship, 
            data = data, 
            subset = (treated == FALSE))
se_3_1  <- coeftest(ols_3_1, vcov = vcovHC(ols_3_1, type = "HC1"))

ols_3_2 <- lm(formula = b ~ age_35_52 + age_53_plus + female + high_education + high_income + 
    married + parentship + high_temperature + high_usage + high_general_risk + 
    high_weather_risk + high_accuracy + high_credibility, 
            data = data, 
            subset = (treated == FALSE))
se_3_2  <- coeftest(ols_3_2, vcov = vcovHC(ols_3_2, type = "HC1"))

ols_3_3 <- lm(formula = a ~ age_35_52 + age_53_plus + female + high_education + high_income + 
    married + parentship, 
            data = data, 
            subset = (treated == FALSE))
se_3_3  <- coeftest(ols_3_3, vcov = vcovHC(ols_3_3, type = "HC1"))

ols_3_4 <- lm(formula = a ~ age_35_52 + age_53_plus + female + high_education + high_income + 
    married + parentship + high_temperature + high_usage + high_general_risk + 
    high_weather_risk + high_accuracy + high_credibility, 
            data = data, 
            subset = (treated == FALSE))
se_3_4  <- coeftest(ols_3_4, vcov = vcovHC(ols_3_4, type = "HC1"))

se_3 <- list(se_3_1[,2], se_3_2[,2], se_3_3[,2], se_3_4[,2])
p_3  <- list(se_3_1[,4], se_3_2[,4], se_3_3[,4], se_3_4[,4])

stargazer(ols_3_1, ols_3_2, ols_3_3, ols_3_4, 
          align = TRUE, 
          se = se_3, 
          p = p_3,   
          title = "Linear regressions: Explanatory analysis of Ambiguity Indices b and a",
          covariate.labels = c("age(35-52)",
                               "age(53-69)",
                               "gender (female)",
                               "high education",
                               "high income",
                               "family (married or same sex union)",
                               "parentship",
                               "high temperature (median)",
                               "high weather forecast usage (median)",
                               "high general risk attitude (median)",
                               "high weather risk attitude (median)",
                               "high accuracy (median)",
                               "high credibility (median)",
                               "Constant"), 
          font.size = "scriptsize",
          type = "html", 
          df = FALSE,
          style = "qje")

**Linear regressions: Explanatory analysis of Ambiguity Indices b and a**

	b		a
	(1)	(2)	(3)	(4)

age(35-52)	-0.004	-0.001	0.065^*	0.050
	(0.021)	(0.021)	(0.037)	(0.036)

age(53-69)	-0.047^**	-0.043^*	0.149^***	0.139^***
	(0.023)	(0.023)	(0.038)	(0.037)

gender (female)	-0.064^***	-0.055^***	0.037	0.040
	(0.017)	(0.017)	(0.027)	(0.027)

high education	-0.071^***	-0.072^***	0.022	0.025
	(0.018)	(0.018)	(0.028)	(0.028)

high income	0.024	0.019	0.018	0.027
	(0.017)	(0.017)	(0.030)	(0.031)

family (married or same sex union)	-0.019	-0.017	-0.056^*	-0.059^*
	(0.019)	(0.019)	(0.032)	(0.033)

parentship	0.020	0.016	-0.054^*	-0.052^*
	(0.020)	(0.020)	(0.030)	(0.030)

high temperature (median)		-0.022		-0.074^***
		(0.016)		(0.027)

high weather forecast usage (median)		-0.016		-0.008
		(0.016)		(0.026)

high general risk attitude (median)		0.028		-0.010
		(0.018)		(0.027)

high weather risk attitude (median)		0.025		-0.028
		(0.018)		(0.028)

high accuracy (median)		-0.025		-0.010
		(0.022)		(0.035)

high credibility (median)		0.007		-0.046
		(0.017)		(0.029)

Constant	0.013	0.017	0.656^***	0.759^***
	(0.023)	(0.034)	(0.039)	(0.053)

N	1,361	1,361	1,361	1,361
R²	0.028	0.036	0.015	0.024
Adjusted R²	0.023	0.026	0.009	0.015
Residual Std. Error	0.289	0.289	0.480	0.479
F Statistic	5.550^***	3.835^***	2.845^***	2.542^***

Notes:	^***Significant at the 1 percent level.
	^**Significant at the 5 percent level.
	^*Significant at the 10 percent level.

  # stargazer(ols_1, ols_2, ols_3, ols_4, ols_5, ols_6, 
  #           align = TRUE, 
  #           se = se, 
  #           p = p,   
  #           title = "Linear regressions: Treatment effects on b",
  #           model.names = FALSE,
  #           column.labels = c("full", "confirmation", "contradiction", "point", "interval", "both"),
  #           covariate.labels = c("contradiction", "both", "interval", "part2", "contradiction x stage 2", "both x stage2", "interval x stage2", "Constant"),
  #           font.size = "scriptsize",
  #           type = "html", 
  #           df = FALSE,
  #           style = "qje")

3.4 Table 4

ols_4_1 <- lm(formula = b ~ surprise + treated + surprise*treated, 
            data = data)
se_4_1  <- coeftest(x = ols_4_1, 
                    vcov = vcovCL(ols_4_1,
                                  cluster = ~data$participant.label,
                                  type = "HC1"))

ols_4_2 <- lm(formula = b ~ communication + treated + communication*treated, 
            data = data,
            subset = (surprise == FALSE))
se_4_2  <- coeftest(x = ols_4_2, 
                    vcov = vcovCL(ols_4_2,
                                  cluster = data[surprise == FALSE, participant.label],
                                  type = "HC1"))

ols_4_3 <- lm(formula = b ~ communication + treated + communication*treated, 
            data = data,
            subset = (surprise == TRUE))
se_4_3  <- coeftest(x = ols_4_3, 
                    vcov = vcovCL(ols_4_3,
                                  cluster = data[surprise == TRUE, participant.label],
                                  type = "HC1"))

ols_4_4 <- lm(formula = b ~ surprise + treated + surprise*treated, 
            data = data,
            subset = (communication == "point"))
se_4_4  <- coeftest(x = ols_4_4, 
                    vcov = vcovCL(ols_4_4,
                                  cluster = data[communication == "point", participant.label],
                                  type = "HC1"))

ols_4_5 <- lm(formula = b ~ surprise + treated + surprise*treated, 
            data = data,
            subset = (communication == "interval"))
se_4_5  <- coeftest(x = ols_4_5, 
                    vcov = vcovCL(ols_4_5,
                                  cluster = data[communication == "interval", participant.label],
                                  type = "HC1"))

ols_4_6 <- lm(formula = b ~ surprise + treated + surprise*treated, 
            data = data,
            subset = (communication == "both"))
se_4_6  <- coeftest(x = ols_4_6, 
                    vcov = vcovCL(ols_4_6,
                                  cluster = data[communication == "both", participant.label],
                                  type = "HC1"))

se_4 <- list(se_4_1[,2], se_4_2[,2], se_4_3[,2], se_4_4[,2], se_4_5[,2], se_4_6[,2])
p_4  <- list(se_4_1[,4], se_4_2[,4], se_4_3[,4], se_4_4[,4], se_4_5[,4], se_4_6[,4])

stargazer(ols_4_1, ols_4_2, ols_4_3, ols_4_4, ols_4_5, ols_4_6, 
          align = TRUE, 
          se = se_4, 
          p = p_4,   
          title = "Linear regressions: Treatment effects on ambiguity index b",
          font.size = "scriptsize",
          type = "html", 
          df = FALSE)

**Linear regressions: Treatment effects on ambiguity index b**

	Dependent variable:

	b
	(1)	(2)	(3)	(4)	(5)	(6)

surprise	0.002			0.012	-0.014	0.007
	(0.015)			(0.026)	(0.027)	(0.027)

communicationinterval		-0.017	-0.043
		(0.025)	(0.027)

communicationboth		-0.038	-0.043
		(0.025)	(0.027)

treated	-0.020^**	-0.041^***	-0.0002	-0.041^***	-0.010	-0.008
	(0.008)	(0.014)	(0.014)	(0.014)	(0.014)	(0.015)

surpriseTRUE:treated	0.014			0.041^**	0.016	-0.015
	(0.012)			(0.020)	(0.020)	(0.020)

communicationinterval:treated		0.031	0.006
		(0.020)	(0.020)

communicationboth:treated		0.034	-0.023
		(0.021)	(0.020)

Constant	-0.068^***	-0.050^***	-0.037^*	-0.050^***	-0.067^***	-0.087^***
	(0.010)	(0.017)	(0.019)	(0.017)	(0.019)	(0.019)


Observations	3,010	1,490	1,520	1,014	1,002	994
R²	0.001	0.003	0.006	0.005	0.0003	0.001
Adjusted R²	-0.0002	-0.001	0.002	0.003	-0.003	-0.002
Residual Std. Error	0.310	0.300	0.320	0.299	0.317	0.315
F Statistic	0.770	0.819	1.694	1.851	0.083	0.244

Note:	p<0.1; p<0.05; p<0.01

3.5 Table 5

ols_5_1 <- lm(formula = a ~ surprise + treated + surprise*treated,
              data = data)
se_5_1  <- coeftest(x = ols_5_1, 
                    vcov = vcovCL(ols_5_1,
                                  cluster = ~data$participant.label,
                                  type = "HC1"))

ols_5_2 <- lm(formula = a ~ communication + treated + communication*treated,
              data = data,
              subset = (surprise == FALSE))
se_5_2  <- coeftest(x = ols_5_2, 
                    vcov = vcovCL(ols_5_2,
                                  cluster = data[surprise == FALSE, participant.label],
                                  type = "HC1"))

ols_5_3 <- lm(formula = a ~ communication + treated + communication*treated,
              data = data,
              subset = (surprise == TRUE))
se_5_3  <- coeftest(x = ols_5_3, 
                    vcov = vcovCL(ols_5_3,
                                  cluster = data[surprise == TRUE, participant.label],
                                  type = "HC1"))

ols_5_4 <- lm(formula = a ~ surprise + treated + surprise*treated, 
              data = data,
              subset = (communication == "point"))
se_5_4  <- coeftest(x = ols_5_4, 
                    vcov = vcovCL(ols_5_4,
                                  cluster = data[communication == "point", participant.label],
                                  type = "HC1"))

ols_5_5 <- lm(formula = a ~ surprise + treated + surprise*treated, 
              data = data,
              subset = (communication == "interval"))
se_5_5  <- coeftest(x = ols_5_5, 
                    vcov = vcovCL(ols_5_5,
                                  cluster = data[communication == "interval", participant.label],
                                  type = "HC1"))

ols_5_6 <- lm(formula = a ~ surprise + treated + surprise*treated, 
              data = data,
              subset = (communication == "both"))
se_5_6  <- coeftest(x = ols_5_6, 
                    vcov = vcovCL(ols_5_6,
                                  cluster = data[communication == "both", participant.label],
                                  type = "HC1"))

se_5 <- list(se_5_1[,2], se_5_2[,2], se_5_3[,2], se_5_4[,2], se_5_5[,2], se_5_6[,2])
p_5  <- list(se_5_1[,4], se_5_2[,4], se_5_3[,4], se_5_4[,4], se_5_5[,4], se_5_6[,4])

stargazer(ols_5_1, ols_5_2, ols_5_3, ols_5_4, ols_5_5, ols_5_6, 
          align = TRUE, 
          se = se_5, 
          p = p_5,   
          title = "Linear regressions: Treatment effects on ambiguity index a",
          font.size = "scriptsize",
          type = "html", 
          df = FALSE)

**Linear regressions: Treatment effects on ambiguity index a**

	Dependent variable:

	a
	(1)	(2)	(3)	(4)	(5)	(6)

surprise	-0.045^*			0.002	-0.046	-0.092^**
	(0.025)			(0.044)	(0.045)	(0.041)

communicationinterval		0.023	-0.026
		(0.045)	(0.044)

communicationboth		0.063	-0.030
		(0.043)	(0.041)

treated	-0.007	0.023	-0.022	0.023	-0.004	-0.041
	(0.020)	(0.036)	(0.033)	(0.036)	(0.033)	(0.033)

surpriseTRUE:treated	0.007			-0.044	0.006	0.061
	(0.027)			(0.049)	(0.046)	(0.046)

communicationinterval:treated		-0.027	0.024
		(0.049)	(0.046)

communicationboth:treated		-0.064	0.042
		(0.049)	(0.046)

Constant	0.740^***	0.712^***	0.714^***	0.712^***	0.734^***	0.775^***
	(0.018)	(0.031)	(0.031)	(0.031)	(0.033)	(0.030)


Observations	3,010	1,490	1,520	1,014	1,002	994
R²	0.002	0.001	0.0004	0.001	0.002	0.005
Adjusted R²	0.001	-0.002	-0.003	-0.002	-0.001	0.002
Residual Std. Error	0.513	0.516	0.512	0.515	0.535	0.490
F Statistic	1.647	0.405	0.123	0.285	0.549	1.639

Note:	p<0.1; p<0.05; p<0.01

3.6 Table 6

ols_6_1 <- lm(formula = ed ~ surprise, 
            data = data,
            subset = (stage == 2))
se_6_1  <- coeftest(ols_6_1, vcov = vcovHC(ols_6_1, type = "HC1"))

ols_6_2 <- lm(formula = ed ~ communication, 
            data = data,
            subset = (stage == 2 & surprise == FALSE))
se_6_2  <- coeftest(ols_6_2, vcov = vcovHC(ols_6_2, type = "HC1"))

ols_6_3 <- lm(formula = ed ~ communication, 
            data = data,
            subset = (stage == 2 & surprise == TRUE))
se_6_3  <- coeftest(ols_6_3, vcov = vcovHC(ols_6_3, type = "HC1"))

ols_6_4 <- lm(formula = ed ~ surprise, 
            data = data,
            subset = (stage == 2 & communication == "point"))
se_6_4  <- coeftest(ols_6_4, vcov = vcovHC(ols_6_4, type = "HC1"))

ols_6_5 <- lm(formula = ed ~ surprise, 
            data = data,
            subset = (stage == 2 & communication == "interval"))
se_6_5  <- coeftest(ols_6_5, vcov = vcovHC(ols_6_5, type = "HC1"))

ols_6_6 <- lm(formula = ed ~ surprise, 
            data = data,
            subset = (stage == 2 & communication == "both"))
se_6_6  <- coeftest(ols_6_6, vcov = vcovHC(ols_6_6, type = "HC1"))

se_6 <- list(se_6_1[,2], se_6_2[,2], se_6_3[,2], se_6_4[,2], se_6_5[,2], se_6_6[,2])
p_6  <- list(se_6_1[,4], se_6_2[,4], se_6_3[,4], se_6_4[,4], se_6_5[,4], se_6_6[,4])

stargazer(ols_6_1, ols_6_2, ols_6_3, ols_6_4, ols_6_5, ols_6_6, 
          align = TRUE, 
          se = se_6,
          p = p_6,   
          title = "Linear regressions: Treatment effects on Euclidian distance between vector of matching probabilities in part 1 vs. part 2",
          font.size = "scriptsize",
          type = "html", 
          df = FALSE)

**Linear regressions: Treatment effects on Euclidian distance between vector of matching probabilities in part 1 vs. part 2**

	Dependent variable:

	ed
	(1)	(2)	(3)	(4)	(5)	(6)

surprise	6.824^***			10.120^***	2.423	8.023^**
	(1.775)			(3.029)	(3.033)	(3.158)

communicationinterval		0.701	-6.996^**
		(2.933)	(3.126)

communicationboth		1.195	-0.902
		(2.991)	(3.194)

Constant	44.941^***	44.316^***	54.436^***	44.316^***	45.017^***	45.511^***
	(1.224)	(2.001)	(2.274)	(2.001)	(2.144)	(2.223)


Observations	1,505	745	760	507	501	497
R²	0.010	0.0002	0.008	0.022	0.001	0.013
Adjusted R²	0.009	-0.002	0.005	0.020	-0.001	0.011
Residual Std. Error	34.441	33.445	35.337	34.076	33.956	35.205
F Statistic	14.768^***	0.081	2.966^*	11.180^***	0.637	6.453^**

Note:	p<0.1; p<0.05; p<0.01